What car are you choosing? I had only considered the differences between swopping tyres on the same 16" rims, or downsizing to 15" . You can get crossclimates in 205/45/R 17 ,about £150 each. If the dealer wont play ball you could maybe get them fitted independently ,and quite possibly get a fair price on ebay for the new ones that were removed. Especially if you do it immediately while they still have knobbly bits and coloured stripes as new. ( dont let the tyre fitters ,or indeed the main dealer, keep them without a price adjustment

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But if swopping to 16" wheels you would also need to negotiate for different wheels. The dealership might be only too happy to remove and keep 17" wheels and tyres and supply you 4 new (cheaper) 16" Honda wheels with the tyres of your choice. They will gain on the deal. If they are happy with suitability. In fact they may gain so much I personally would still look into the feasibility of buying my own 16" wheels (genuine Honda or aftermarket -maybe after market 17" ) and tyres and keeping the originals,possibly unused, so the car can later be sold as standard with undamaged wheels (they might reduce the trade in value if the car no longer has the 17" wheels expected of that model , and certainly will if they have been kerbed. ) Or flog them ,or the alternative set ,privately.
205/45/R17 have a similar rolling circumference to 185/55/R16 so speedo etc shouldnt be affected much. . Both are Honda sizes, The downside is the tread width is 20 mm narrower. Also 17" rims are wider - 7" so the dealer might have concerns about suitability. And also 185/55/R16 crossclimates are a rare size and cost about £165 each . (195/55/R16 are closer on width and rolling circumference , and only cost about £120 each but these are not an approved Honda size)
The real bargain is downsizing from 16" to 15". 185/60/R15. also a Honda approved size. Crossclimates in this size are only about £100 each. which could go towards the cost of wheels ( assuming 17" to 15" is feasible.) If you buy the initial set of tyres, then replace them once prior to selling the car thats a potential saving of over £500 compared to 8 x 16" tyres. (or you could spend £400 on just one set and never having to replace them because you also get some wear from your summer ones that came with the car) . Over the long term my crazy idea of buying extra wheels makes more sense! Especially if like me you often drive where winter rated tyres are compulsory. P
another option for those who plan to replace tyres at least once during their ownership. Initially run what Honda Brung, be they 16" or 17". and dont involve the dealer . Then as soon as convenient fit 4 new all seasons. But make sure you keep the tyres that were removed ! . Store those tyres, . With a bit of planning, swopping front to rear to even wear, and some luck with the season its possible that the last tyres you need to fit to the car before its sold could be your stored summer tyres. You'd only need to pay for fitting (maybe £15 a corner if you shop around) Even if you dont get the full wear from them, you wont be handing over the car with nearly new tyres you have only just paid for or be tempted to fit cheapo tyres . OK you are paying for new tyres early, but the stored tyres are inflation proof and better than money in the bank (hopefully they will inflate with air when the time comes

) If you get the timing wrong and dont need to fit them you might be able to sell them for more than you paid for the all seasons. A bit of faffing about but may be a solution for some.